Question

How do you solve `|5x-4| +3 = 3`?

Answer 1

See the solution process below:

Explanation:

First, subtract `color(red)(3)` from each side of the equation to isolate the absolute value function while keeping the equation balanced:

`abs(5x - 4) + 3 - color(red)(3) = 3 - color(red)(3)`

`abs(5x - 4) + 0 = 0`

`abs(5x - 4) = 0`

Normally an absolute value equality would produce two answers. However, because the absolute value function is equal to `0` there is only one solution.

We can equate the term within the absolute value to `0` and solve for `x`:

`5x - 4 = 0`

`5x - 4 + color(red)(4) = 0 + color(red)(4)`

`5x - 0 = 4`

`5x = 4`

`(5x)/color(red)(5) = 4/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 4/5`

`x = 4/5`